27 citations · 103 across the 9 of their papers we have counts for
10 papers
Fast Möbius and Zeta Transforms
Tommaso Pegolotti, Bastian Seifert, Markus Püschel
Möbius inversion of functions on partially ordered sets (posets) is a classical tool in combinatorics. For finite posets it consists of two, mutually inverse, linear…
Causal Fourier Analysis on Directed Acyclic Graphs and Posets
Bastian Seifert, Chris Wendler, Markus Püschel
We present a novel form of Fourier analysis, and associated signal processing concepts, for signals (or data) indexed by edge-weighted directed acyclic graphs (DAGs). This means th…
Discrete Signal Processing on Meet/Join Lattices
Markus Püschel, Bastian Seifert, Chris Wendler
A lattice is a partially ordered set supporting a meet (or join) operation that returns the largest lower bound (smallest upper bound) of two elements. Just like graphs, lattices a…
Learning Set Functions that are Sparse in Non-Orthogonal Fourier Bases
Chris Wendler, Andisheh Amrollahi, Bastian Seifert +2
Many applications of machine learning on discrete domains, such as learning preference functions in recommender systems or auctions, can be reduced to estimating a set function tha…
Digraph Signal Processing with Generalized Boundary Conditions
Bastian Seifert, Markus Püschel
Signal processing on directed graphs (digraphs) is problematic, since the graph shift, and thus associated filters, are in general not diagonalizable. Furthermore, the Fourier tran…
Dynamical Component Analysis (DyCA) and its application on epileptic EEG
Katharina Korn, Bastian Seifert, Christian Uhl
Dynamical Component Analysis (DyCA) is a recently-proposed method to detect projection vectors to reduce the dimensionality of multi-variate deterministic datasets. It is based on…
FFT and orthogonal discrete transform on weight lattices of semi-simple Lie groups
Bastian Seifert
We give two algebro-geometric inspired approaches to fast algorithms for Fourier transforms in algebraic signal processing theory based on polynomial algebras in several variables.…
The discrete cosine transform on triangles
Bastian Seifert, Knut Hüper
The discrete cosine transform is a valuable tool in analysis of data on undirected rectangular grids, like images. In this paper it is shown how one can define an analogue of the d…
Fast cosine transform for FCC lattices
Bastian Seifert, Knut Hüper, Christian Uhl
Voxel representation and processing is an important issue in a broad spectrum of applications. E.g., 3D imaging in biomedical engineering applications, video game development and v…
Dynamical Component Analysis (DyCA): Dimensionality Reduction For High-Dimensional Deterministic Time-Series
Bastian Seifert, Katharina Korn, Steffen Hartmann +1
Multivariate signal processing is often based on dimensionality reduction techniques. We propose a new method, Dynamical Component Analysis (DyCA), leading to a classification of t…